We visualize hyperbolic honeycombs using Schläfli symbols.
problem Tiling hyperbolic spaces with efficient Schläfli symbols.
method Develop strategies for visualizing honeycombs in spherical, Euclidean, and hyperbolic spaces.
result Infinitely many hyperbolic honeycombs exist, with various categories of vertices and cells.
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
The study examines topological surfaces using grid structures in Euclidean and hyperbolic spaces.
problem Understanding topological surfaces in geometric spaces.
method Using gridded surfaces in cubic honeycombs of Euclidean and hyperbolic spaces.
result Topological surfaces can be represented as gridded structures in these spaces.
Sharp decay estimates for critical Dirac equations on \(\mathbb{R}^n\).
problem Analyzing decay behavior of critical Dirac equations.
method Proving sharp pointwise decay estimates.
result Explicit asymptotic behavior of excited states in honeycomb structures.
Project aims to diagnose and track IPF disease using deep learning.
problem Diagnosing and tracking IPF disease in lung images.
method Developed a deep learning model for identifying honeycombing and ground glass patterns in HRCT lung images.
result Deep learning model achieved high accuracy in identifying specific lung regions.
We introduce a new discrete system that arises from ellipsoidal billiards and is closely related to the double reflection nets. The system is defined on the lattice of a uniform honeycomb consisting of rectified hypercubes and cross polytopes. In the 2-dimensional case, the lattice is regular and it incorporates dyna…
It is known that every ribbon category with unimodality allows symmetrized 6j-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category E. We define the mirror conjugate symmetry of 6j-symbols instead and sho…
Smooth manifolds can be triangulated with graphs of bounded twin-width.
problem Understanding the structure of triangulations of smooth manifolds.
method Using Whitney's triangulation method and bounding the twin-width of specific graphs.
result Compact smooth manifolds have triangulations with graphs of bounded twin-width.
We provide a measure based topology for certain unions of C2 rectifiable submanifolds of mixed dimensions in Rn. In this topology lower dimensional sets remain in the limit as measures when higher dimensional sets collapse down to them. For example a decreasing sequence of spheres may have a limit consisting of just a …
Paper proposes a weak supervision technique for CNN semantic segmentation of lung diseases using partially annotated data.
problem Creating annotated datasets for semantic segmentation of lung diseases is laborious and time-consuming.
method Proposes a weak supervision technique that utilizes partially annotated datasets to improve CNN semantic segmentation accuracy.
result Significantly improved segmentation accuracy using partially annotated datasets.
Quantum phase diagrams for Chern topological insulators show jumps at critical loci.
problem Understanding phase transitions in Chern topological insulators.
method Mathematical formulation and explicit families of physical systems.
result Synthetic design of arbitrary Chern jumps in topological phases.
3D self-affine tiles with specific digit sets have boundary homeomorphic to a 2-sphere.
problem Characterizing 3D self-affine tiles with collinear digit sets whose boundary is a sphere.
method Using lattice tiling combinatorics and topological properties of spheres, the paper characterizes such tiles.
result The boundary of these tiles is homeomorphic to a 2-sphere under certain conditions.